Answer:
Period = [tex]\frac{2}{3}[/tex]
The ferris wheel will complete one round in 40 seconds.
Step-by-step explanation:
We are given the function representing the height of the wheel by,
[tex]h=82.5\sin 3\pi (t+0.5)+97.5[/tex] where t = time in minutes.
Now, we know that if a function f(x) has period P, then a×f(bx+c)+d will have the period [tex]\frac{P}{|b|}[/tex].
Since, the function [tex]\sin x[/tex] has period [tex]2\pi[/tex], thus the function h will have period [tex]\frac{2\pi}{3\pi}[/tex] i.e. [tex]\frac{2}{3}[/tex].
Therefore, the period of this function is [tex]\frac{2}{3}[/tex].
Now, since the period is [tex]\frac{2}{3}[/tex] minutes i.e 40 seconds.
Hence, we get that the ferris wheel will complete one round in 40 seconds.
